リング状の質量をつけた円板及び円輪の振動

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The loudspeaker with flat diaphragm as vibrating plate may have many superior qualities, but there occur resonances in the comparatively low frequency range because of lack of rigidity of flat diaphragm. Advantageous for suppressing the resonances is a 'multi-drive' loudspeaker, of which diaphragm is driven by plural voice-coils, and the driving forces are adjusted so as to cancel the resonances. If the diaphragm is driven by a voice-coil(or voice-coils) attached to the nodes of an undesirable vibration mode, that vibration mode will be small because of a large driving-point impedance at the nodes. However, it is necessary to find the effect of the mass of voice-coil on the eigenfrequencies and eigenfunctions of other vibration modes, for example, in order to determine the ratio of driving forces. Eigenfunctions of a circular plate with a voice-coil(or voice-coils) are expanded by the well-known eigenfunction {P_m(r)} of a plate with no voice-coil. After several operations, eigenfrequencies{ω_<cm>} of the vibration of a plate with a voice-coil are expressed in the form of matrix, as a function of the eigenfrequencies {ω_m}, values of eigenfunctions at voice-coil positions P_m(r_1), and the mass of voice-coil to mass of plate ratio, of a circular plate with no voice-coil. Eigenfrequencies of a circular plate with plural voice-coils can be computed with considerable ease, and it can be seen from the matrix expression that, when the voice-coils are attached to nodal circles of the vibration modes of a circular plate with no coil, the eigenfunctions and eigenfrequencies of that mode do not change at all. We calculated eigenvalues k_ma of a circular plate with a single voice-coil of various radiuses and masses, then calculated the eigenfunctions of a circular plate with one or two of voice-coils attached to the nodal circles of the plate. In addition, we calculated eigenvalues of an annular plate with a aingle voice-coil of various radiuses and masses, then calculated the eigenfunctions of an annular plate with a single voice-coil, attached to nodal circle thereof. The results obtained show that, when the position of the voice-coil goes far from the nodal ciecle, eigenvalues decrease, proportionally to the mass of the voice-coil and the displacement of the plate at the voice-coil position. In a circular plate and an annular, plate, free at their boundaries, the law of `Conservation of Momentum' is satisfied, including the momentum of voice-coil. That is to say, eigenfunctions make such a change that the change of the momentum of the plate cancels that of momentum due to the mass of voice-coil. Thus, the larger are the mass of voice-coil and the displacement of the plate, at the voice-coil position, the greater is the change of eigenfunctions. The force-ratio of the voil-coils to suppress the first and second resonances simultaneously, is obtained from the displacements of the first resonance mode at the position of the secondary nodes of the plate. The mass ratio between the two voice-coils can be selected in such a manner that the first eigenfunction becomes nearly equal to that of the plate with no voice-coil.
社団法人日本音響学会の論文
1978-08-01

リング状の質量をつけた円板及び円輪の振動

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